The problem is that with the medallion system, you're turning the ability to drive a cab into property. As such, it becomes a /lot/ harder to reasonably control supply, because adding medallions will garner protests from the existing holders, regardless of the needs of the city. Additionally, with the costs of these medallions, it becomes a lot harder for a middle class person to get started in the taxi business; you have to join one of the cartels and curry favor with them in order to have a chance to drive and get decent dispatches.
I'd argue that the best way to handle the taxi drivers of all sorts is to move to a licensing system. Give priority to existing drivers, but at the same time, allow flexibility in setting the supply to give the little guy a chance to compete. Taxi systems in most city are corrupt from top to bottom, and these actions in France just show how the drivers are willing to go along with the broken system at hand.
I came to realize a system like medallions were needed when seeing taxis clog traffic after venues with well paying customers were over. Supply is far more than demand in these cases, and even apps with scheduling won't keep the streets from being clogged beyond reason.
Humans are a funny bunch who overall suck are cooperation, specially when trying the role of a worker ant.
That sounds like a traffic control problem, a public transportation problem, and an event planning problem related to specific events rather than a need for medallions.
Once the people are already there, they need to get home somehow -- what do you expect? How do fewer taxis help the problem?
"That sounds like a traffic control problem, a public transportation problem.."
All those things come into play when regulating how many registered taxis are allowed on the street. Or the decision to regulate at all. Also its one of the sticking points for locales as to why they want to regulate operators like Uber as local planners need to be aware of them and their numbers.
"..and an event planning problem related to specific events"
The venues don't really have a say in who parks out in public streets, they can raise complaints if it becomes a problem though and often try to cash in by hiring services themselves. The more monied customers will most likely not ride the meat bus over to a public transit hub though.
A licensing system would be more flexible there, as you could have categories of licenses to handle different types of demand -- rush hour taxis, etc. With a medallion system, every holder has a heavy financial incentive for their cab to be in service 24/7, due to its very high cost, meaning that during special events, you can and will get an excess in cabs.
I'd argue that the best way to handle the taxi drivers of all sorts is to move to a licensing system. Give priority to existing drivers, but at the same time, allow flexibility in setting the supply to give the little guy a chance to compete. Taxi systems in most city are corrupt from top to bottom, and these actions in France just show how the drivers are willing to go along with the broken system at hand.